# Linear Algebra projection

• May 9th 2012, 04:23 PM
Kiefer
Linear Algebra projection
Suppose E is a projection in M_2(C) with rank one. Show that there is a real number θ and a complex number β with |β| = 1 such that
E =
cos^2 βsinθcosθ
Bsinθcosθ sin^2 θ

M_2(C) represents an 2 x 2 matrix in the complex numbers.
Β represents β conjugate.
• May 9th 2012, 06:29 PM
HallsofIvy
Re: Linear Algebra projection
It's impossible to be sure what you mean. Is it
$\begin{pmatrix}cos^2(\theta) & \beta sin(\theta)cos(\theta) \\ \overline{\beta}sin(\theta)cos(\theta) & sin^2(\theta)\end{pmatrix}$
?